Classical & quantum dynamics of information and entanglement properties of fermion systems

Abstract

Due to their great importance, both from the fundamental and from the practical points of view, it is imperative that the various facets of the concepts of information and entanglement are explored systematically in connection with diverse physical systems and processes. These concepts are at the core of the emerging field of the Physics of Information. In this Thesis I investigate some aspects of the dynamics of information in both classical and quantum mechanical systems and then move on to explore entanglement in fermion systems by searching for novel ways to classify and quantify entanglement in fermionic systems. In Chapter 1 a brief review of the different information and entropic measures as well as of the main evolution equations of classical dynamical and quantum mechanical systems is given. The conservation of information as a fundamental principle both at the classical and quantum levels, and the implications of Landauer's theorem are discussed in brief. An alternative and more intuitive proof of the no-broadcasting theorem is also provided. Chapter 2 is a background chapter on quantum entanglement, where the differences between the concept of entanglement in systems consisting of distinguishable subsystems and the corresponding concept in systems of identical fermions are emphasized. Different measures of entanglement and relevant techniques such as majorization, are introduced. To illustrate some of the concepts reviewed here I discuss the entanglement properties of an exactly soluble many-body model which was studied in paper (E) of the publication list corresponding to the present Thesis. An alternative approach to the characterization of quantum correlations, based on perturbations under local measurements, is also briefly reviewed. The use of uncertainty relations as entanglement indicators in composite systems having distinguishable subsystems is then examined in some detail. Chapter 3 is based on papers (A) and (B) of the list of publications. Extended Landauer-like principles are developed, based amongst others on the conservation of information of divergenceless dynamical systems. Conservation of information within the framework of general probabilistic theories, which include the classical and quantum mechanical probabilities as particular instances, is explored. Furthermore, Zurek's information transfer theorem and the no-deleting theorem are generalized. Chapter 4 is based on articles (C) and (D) mentioned in the publication list, and investigates several separability criteria for fermions. Criteria for the detection of entanglement are developed based either on the violation of appropriate uncertainty relations or on inequalities involving entropic measures. Chapter 5 introduces an approach for the characterization of quantum correlations (going beyond entanglement) in fermion systems based upon the state disturbances generated by the measurement of local observables. Chapter 6 summarizes the conclusions drawn in the previous chapters. The work leading up to this Thesis has resulted in five publications in peer reviewed science research journals.